What can be said about publishing mathematical papers on e.g. viXra if the motivation is its low barriers and lack of experience with publishing papers and the idea behind it is to build up a reputation, provided the content of the publication suffices that purpose.

Can that way of getting a foot into the door of publishing be recommended or would it be better to resort to polishing door knobs at arXiv to get an endorsement?

Personal experience or that of someone you know would of course also be interesting to me.

$\begingroup$Neither the ArXiv nor viXra, nor for that matter, posting on your personal website, count as a mathematical publication that enhance or detract from one's reputation. Publication in a reputable peer reviewed mathematics journal counts. (Accepted for publication also counts, given the long lag time between acceptance and publication. Accepted pending revision is almost as good. Under review does not count.) A paper posted on the ArXiv may be studied by others in your field, so that can help build reputation. Posting papers on viXra and putting them on your CV could be harmful.$\endgroup$
– Joe SilvermanMay 20 at 18:23

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$\begingroup$arXiv and viXra shouldn't really be mentioned in the same sentence. The arXiv has a system so that not just anyone can submit, and what is submitted should look like a serious research paper (not checked for accuracy, but should at least superficially look professional). Anyone can submit to viXra and the standards are much, much lower. As in, it accepts stuff that looks like a bad, fail-grade school project.$\endgroup$
– David RobertsMay 21 at 3:46

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$\begingroup$If your work is arXivable, and you should be able to tell by comparing it to other papers in your field that appear there, you should really try and hunt down someone to endorse you. Once the paper is on the arXiv, you then have a better chance of getting other mathematicians to look at it if you email them. Getting over the minimal barrier that the arXiv has means that they can give more of a benefit of the doubt to an unannounced email referring to an unpublished paper from a relatively unknown author. Saying "read my attached paper" or "look at this viXra link" is a bit of a red flag; ...$\endgroup$
– David RobertsMay 21 at 7:27

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$\begingroup$...whereas saying "you might be interested in my recent arXiv preprint 20xx.?????" means they only have to overcome their own lack of time.$\endgroup$
– David RobertsMay 21 at 7:29

2 Answers
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Yes, the place of publication can absolutely hurt your reputation. Specifically, I can tell you from having served on many hiring committees (and from conversations with professors at other universities about their hiring committees and tenure processes), that publications in predatory journals can hurt you. I'm talking specifically about journals whose model is to get the author to pay them, and whose peer review standards are a joke. Publications in journals like that can be interpreted as an author trying to side-step the normal process, or unethically inflate their numbers.

It may be hard to break into the absolute top journals with your first few papers (unless you have a famous advisor/coauthor or went to a prestigious school). But there are plenty of good journals around and after a track record of publishing in good journals you will have less difficulty publishing in top journals (of course, it'll always be extremely hard to publish in the Annals and other super elite journals). For people starting out, I recommend at least checking Beall's list of predatory publishers to be sure you don't end up publishing somewhere that might be frowned upon later in your career. Also, don't let fear paralyze you from trying. Lots of editors and referees will go gently on new PhDs. I wish this was even more common, rather than pushing young people out of academia.

$\begingroup$"unless you have a famous advisor/coauthor or went to a prestigious school" <--- yes. I wonder why...$\endgroup$
– David RobertsMay 21 at 3:33

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$\begingroup$@DavidRoberts maybe because that's the next best replacement for the former criterion of being of noble descent to be admiited to a gentlemen's club.$\endgroup$
– Manfred WeisMay 21 at 12:03

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$\begingroup$"unless you have a famous advisor/coauthor or went to a prestigious school" > shouldn't this be "unless you have produced outstanding scientific results"...?$\endgroup$
– EarthliŋMay 21 at 16:55

If you want to build a reputation as a mathematician, post your preprint on the arXiv (this is a preprint server, not counted as publication, the posts are not refereed, and there are essentially no "barriers").

Then send your paper to a mainstream mathematical journal. Avoid those journals which are not reviewed in Mathscinet.
(Recently, many journals proliferated which do not really referee papers, but charge the authors for publication. Avoid them, if you want to build a reputation. The main criterion of a mainstream journal is that all its papers are reviewed in Mathscinet.) Mathscinet also publishes a rating of journals according to their citation rates. Publication in a highly rated journal (say of the first 100) will probably be good for your reputation,
but the "barriers" there are also high.

Still I believe that one's reputation is based more on the quality of papers, rather then the rating of the journals where they are published.
For example, the reputation of G. Perelman is mainly based on a few preprints
which he posted on the arXiv. He did not care to send them to journals.
This is an extreme example, but it is not unique. My 3-d highest cited paper is published in a volume of conference proceedings which is not even a journal (arXiv did not exist yet). My two most cited papers are in the journals which do not enter the list of 100 top journals according to MSN rating (though I also published in top journals). I conclude that there is very little correlation between the rating of an individual paper and the rating of the journal.

$\begingroup$Pre-2002, "the reputation of G. Perelman [was] mainly based" on his proof of the Soul Conjecture, published in the Journal of Differential Geometry, a rather exclusive outlet, and work on spaces whose curvature is bounded below (which he spoke on at the 1994 Zurich ICM), published in places like JAMS.$\endgroup$
– David RobertsMay 21 at 3:18

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$\begingroup$Sure, but he could only get away with that because he had a strong reputation to start with (ICM speaker!), and he then managed to solve a once-in-a-century problem. This is not a good example for someone who is asking about basic facts of the informal academic reputation system.$\endgroup$
– David RobertsMay 21 at 3:25

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$\begingroup$In complement to David Roberts' comment: I remember that when Perelman posted his papers on arXiv (Nov. 2002 to July 2003), I was told it was taken very seriously, based on his reputation. And obviously at that time, it meant his reputation prior to the arXiv preprints, which was based on published papers (and probably further mathematician activity, but published papers is the easiest/laziest clue to detect now).$\endgroup$
– YCorMay 21 at 12:11

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$\begingroup$regarding "there are essentially no barriers": [Tsang, Sandro. (2020). Re: How to get endorsement in arXiv?] (researchgate.net/post/How_to_get_endorsement_in_arXiv/…) tells a different story for people that are in my situation, namely not affiliated with a research institution and no network of supportive arXiv endorsers$\endgroup$
– Manfred WeisMay 21 at 12:17

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$\begingroup$I agree with Manfred Weis's comment about barriers. See also my comment under the question itself, and this MO question.$\endgroup$
– Timothy ChowMay 21 at 14:39